Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,3,Mod(19,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.f (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.94278685509\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 91.3 | ||
Root | \(-0.710719 - 1.86946i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.91 |
Dual form | 108.3.f.c.19.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.710719 | − | 1.86946i | −0.355359 | − | 0.934730i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.98976 | + | 2.65732i | −0.747439 | + | 0.664330i | ||||
\(5\) | −1.35609 | + | 2.34881i | −0.271218 | + | 0.469763i | −0.969174 | − | 0.246378i | \(-0.920760\pi\) |
0.697956 | + | 0.716140i | \(0.254093\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.0431 | + | 5.79837i | −1.43473 | + | 0.828339i | −0.997476 | − | 0.0710013i | \(-0.977381\pi\) |
−0.437249 | + | 0.899340i | \(0.644047\pi\) | |||||||
\(8\) | 7.09263 | + | 3.70062i | 0.886579 | + | 0.462578i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.35481 | + | 0.865806i | 0.535481 | + | 0.0865806i | ||||
\(11\) | −8.54822 | + | 4.93532i | −0.777111 | + | 0.448665i | −0.835406 | − | 0.549634i | \(-0.814767\pi\) |
0.0582943 | + | 0.998299i | \(0.481434\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.296185 | − | 0.513008i | 0.0227835 | − | 0.0394622i | −0.854409 | − | 0.519601i | \(-0.826080\pi\) |
0.877192 | + | 0.480139i | \(0.159414\pi\) | |||||||
\(14\) | 17.9776 | + | 14.6541i | 1.28412 | + | 1.04672i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.87730 | − | 15.8895i | 0.117331 | − | 0.993093i | ||||
\(17\) | 8.87968 | 0.522334 | 0.261167 | − | 0.965294i | \(-0.415893\pi\) | ||||
0.261167 | + | 0.965294i | \(0.415893\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 14.0989i | 0.742046i | 0.928624 | + | 0.371023i | \(0.120993\pi\) | ||||
−0.928624 | + | 0.371023i | \(0.879007\pi\) | |||||||
\(20\) | −2.18718 | − | 10.6259i | −0.109359 | − | 0.531297i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 15.3018 | + | 12.4729i | 0.695535 | + | 0.566952i | ||||
\(23\) | −18.2754 | − | 10.5513i | −0.794583 | − | 0.458753i | 0.0469902 | − | 0.998895i | \(-0.485037\pi\) |
−0.841574 | + | 0.540142i | \(0.818370\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.82205 | + | 15.2802i | 0.352882 | + | 0.611209i | ||||
\(26\) | −1.16955 | − | 0.189102i | −0.0449828 | − | 0.00727316i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 14.6182 | − | 44.0234i | 0.522080 | − | 1.57226i | ||||
\(29\) | −10.1764 | − | 17.6260i | −0.350910 | − | 0.607793i | 0.635499 | − | 0.772101i | \(-0.280794\pi\) |
−0.986409 | + | 0.164308i | \(0.947461\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −14.3357 | − | 8.27670i | −0.462441 | − | 0.266990i | 0.250629 | − | 0.968083i | \(-0.419362\pi\) |
−0.713070 | + | 0.701093i | \(0.752696\pi\) | |||||||
\(32\) | −31.0390 | + | 7.78342i | −0.969968 | + | 0.243232i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.31095 | − | 16.6002i | −0.185616 | − | 0.488241i | ||||
\(35\) | − | 31.4524i | − | 0.898641i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −40.6557 | −1.09880 | −0.549401 | − | 0.835559i | \(-0.685144\pi\) | ||||
−0.549401 | + | 0.835559i | \(0.685144\pi\) | |||||||
\(38\) | 26.3573 | − | 10.0203i | 0.693613 | − | 0.263693i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −18.3103 | + | 11.6409i | −0.457758 | + | 0.291022i | ||||
\(41\) | −21.2177 | + | 36.7502i | −0.517506 | + | 0.896346i | 0.482288 | + | 0.876013i | \(0.339806\pi\) |
−0.999793 | + | 0.0203330i | \(0.993527\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 32.2385 | − | 18.6129i | 0.749732 | − | 0.432858i | −0.0758649 | − | 0.997118i | \(-0.524172\pi\) |
0.825597 | + | 0.564260i | \(0.190838\pi\) | |||||||
\(44\) | 12.4424 | − | 37.4708i | 0.282782 | − | 0.851609i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.73658 | + | 41.6642i | −0.146447 | + | 0.905743i | ||||
\(47\) | 1.57134 | − | 0.907211i | 0.0334327 | − | 0.0193024i | −0.483191 | − | 0.875515i | \(-0.660522\pi\) |
0.516623 | + | 0.856213i | \(0.327189\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 42.7423 | − | 74.0318i | 0.872291 | − | 1.51085i | ||||
\(50\) | 22.2958 | − | 27.3524i | 0.445916 | − | 0.547048i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.477704 | + | 2.32083i | 0.00918662 | + | 0.0446313i | ||||
\(53\) | 21.1005 | 0.398122 | 0.199061 | − | 0.979987i | \(-0.436211\pi\) | ||||
0.199061 | + | 0.979987i | \(0.436211\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 26.7709i | − | 0.486744i | ||||||
\(56\) | −92.6894 | + | 3.96007i | −1.65517 | + | 0.0707155i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −25.7186 | + | 31.5515i | −0.443423 | + | 0.543991i | ||||
\(59\) | 76.6879 | + | 44.2758i | 1.29980 | + | 0.750437i | 0.980369 | − | 0.197174i | \(-0.0631764\pi\) |
0.319427 | + | 0.947611i | \(0.396510\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 36.4925 | + | 63.2069i | 0.598238 | + | 1.03618i | 0.993081 | + | 0.117431i | \(0.0374657\pi\) |
−0.394843 | + | 0.918749i | \(0.629201\pi\) | |||||||
\(62\) | −5.28433 | + | 32.6823i | −0.0852311 | + | 0.527134i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 36.6108 | + | 52.4943i | 0.572043 | + | 0.820223i | ||||
\(65\) | 0.803307 | + | 1.39137i | 0.0123586 | + | 0.0214057i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 38.3110 | + | 22.1189i | 0.571807 | + | 0.330133i | 0.757871 | − | 0.652405i | \(-0.226240\pi\) |
−0.186064 | + | 0.982538i | \(0.559573\pi\) | |||||||
\(68\) | −26.5481 | + | 23.5961i | −0.390413 | + | 0.347002i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −58.7990 | + | 22.3538i | −0.839986 | + | 0.319341i | ||||
\(71\) | 111.798i | 1.57462i | 0.616557 | + | 0.787310i | \(0.288527\pi\) | ||||
−0.616557 | + | 0.787310i | \(0.711473\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −76.2003 | −1.04384 | −0.521920 | − | 0.852995i | \(-0.674784\pi\) | ||||
−0.521920 | + | 0.852995i | \(0.674784\pi\) | |||||||
\(74\) | 28.8948 | + | 76.0042i | 0.390470 | + | 1.02708i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −37.4652 | − | 42.1522i | −0.492964 | − | 0.554635i | ||||
\(77\) | 57.2337 | − | 99.1316i | 0.743294 | − | 1.28742i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.30434 | − | 4.79451i | 0.105118 | − | 0.0606901i | −0.446519 | − | 0.894774i | \(-0.647337\pi\) |
0.551637 | + | 0.834084i | \(0.314003\pi\) | |||||||
\(80\) | 34.7757 | + | 25.9570i | 0.434696 | + | 0.324462i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 83.7828 | + | 13.5466i | 1.02174 | + | 0.165203i | ||||
\(83\) | 73.6244 | − | 42.5070i | 0.887041 | − | 0.512133i | 0.0140672 | − | 0.999901i | \(-0.495522\pi\) |
0.872973 | + | 0.487768i | \(0.162189\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.0416 | + | 20.8567i | −0.141666 | + | 0.245373i | ||||
\(86\) | −57.7086 | − | 47.0400i | −0.671030 | − | 0.546977i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −78.8931 | + | 3.37063i | −0.896513 | + | 0.0383026i | ||||
\(89\) | −64.7845 | −0.727916 | −0.363958 | − | 0.931415i | \(-0.618575\pi\) | ||||
−0.363958 | + | 0.931415i | \(0.618575\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.86958i | 0.0754898i | ||||||||
\(92\) | 82.6773 | − | 17.0178i | 0.898666 | − | 0.184976i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.81277 | − | 2.29278i | −0.0299231 | − | 0.0243912i | ||||
\(95\) | −33.1157 | − | 19.1193i | −0.348586 | − | 0.201256i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.59139 | − | 6.22047i | −0.0370246 | − | 0.0641285i | 0.846919 | − | 0.531721i | \(-0.178455\pi\) |
−0.883944 | + | 0.467593i | \(0.845121\pi\) | |||||||
\(98\) | −168.777 | − | 27.2892i | −1.72222 | − | 0.278461i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −66.9803 | − | 22.2412i | −0.669803 | − | 0.222412i | ||||
\(101\) | 55.5037 | + | 96.1353i | 0.549542 | + | 0.951834i | 0.998306 | + | 0.0581840i | \(0.0185310\pi\) |
−0.448764 | + | 0.893650i | \(0.648136\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −79.6133 | − | 45.9648i | −0.772945 | − | 0.446260i | 0.0609793 | − | 0.998139i | \(-0.480578\pi\) |
−0.833924 | + | 0.551879i | \(0.813911\pi\) | |||||||
\(104\) | 3.99918 | − | 2.54251i | 0.0384537 | − | 0.0244472i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.9965 | − | 39.4464i | −0.141476 | − | 0.372136i | ||||
\(107\) | − | 107.741i | − | 1.00693i | −0.864016 | − | 0.503465i | \(-0.832058\pi\) | ||
0.864016 | − | 0.503465i | \(-0.167942\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 86.5562 | 0.794093 | 0.397047 | − | 0.917798i | \(-0.370035\pi\) | ||||
0.397047 | + | 0.917798i | \(0.370035\pi\) | |||||||
\(110\) | −50.0472 | + | 19.0266i | −0.454974 | + | 0.172969i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 73.2793 | + | 170.465i | 0.654279 | + | 1.52201i | ||||
\(113\) | 2.35198 | − | 4.07376i | 0.0208140 | − | 0.0360509i | −0.855431 | − | 0.517917i | \(-0.826708\pi\) |
0.876245 | + | 0.481866i | \(0.160041\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 49.5662 | − | 28.6170i | 0.431010 | − | 0.248844i | ||||
\(116\) | 77.2628 | + | 25.6556i | 0.666059 | + | 0.221169i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 28.2682 | − | 174.833i | 0.239561 | − | 1.48163i | ||||
\(119\) | −89.1793 | + | 51.4877i | −0.749406 | + | 0.432670i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.7852 | + | 20.4126i | −0.0973987 | + | 0.168700i | ||||
\(122\) | 92.2269 | − | 113.144i | 0.755958 | − | 0.927407i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 64.8540 | − | 13.3491i | 0.523016 | − | 0.107654i | ||||
\(125\) | −115.658 | −0.925267 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.37118i | 0.0659148i | 0.999457 | + | 0.0329574i | \(0.0104926\pi\) | ||||
−0.999457 | + | 0.0329574i | \(0.989507\pi\) | |||||||
\(128\) | 72.1160 | − | 105.751i | 0.563406 | − | 0.826180i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.03018 | − | 2.49062i | 0.0156168 | − | 0.0191586i | ||||
\(131\) | −115.067 | − | 66.4338i | −0.878372 | − | 0.507129i | −0.00825098 | − | 0.999966i | \(-0.502626\pi\) |
−0.870121 | + | 0.492837i | \(0.835960\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −81.7506 | − | 141.596i | −0.614666 | − | 1.06463i | ||||
\(134\) | 14.1220 | − | 87.3413i | 0.105388 | − | 0.651800i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 62.9803 | + | 32.8603i | 0.463090 | + | 0.241620i | ||||
\(137\) | −22.5579 | − | 39.0715i | −0.164656 | − | 0.285193i | 0.771877 | − | 0.635772i | \(-0.219318\pi\) |
−0.936533 | + | 0.350579i | \(0.885985\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 130.744 | + | 75.4848i | 0.940601 | + | 0.543056i | 0.890149 | − | 0.455670i | \(-0.150600\pi\) |
0.0504522 | + | 0.998726i | \(0.483934\pi\) | |||||||
\(140\) | 83.5792 | + | 94.0351i | 0.596994 | + | 0.671680i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 209.002 | − | 79.4570i | 1.47184 | − | 0.559556i | ||||
\(143\) | 5.84708i | 0.0408887i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 55.2003 | 0.380692 | ||||||||
\(146\) | 54.1570 | + | 142.453i | 0.370938 | + | 0.975708i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 121.551 | − | 108.035i | 0.821289 | − | 0.729968i | ||||
\(149\) | −71.3914 | + | 123.653i | −0.479137 | + | 0.829889i | −0.999714 | − | 0.0239255i | \(-0.992384\pi\) |
0.520577 | + | 0.853815i | \(0.325717\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −220.027 | + | 127.033i | −1.45713 | + | 0.841276i | −0.998869 | − | 0.0475407i | \(-0.984862\pi\) |
−0.458263 | + | 0.888817i | \(0.651528\pi\) | |||||||
\(152\) | −52.1746 | + | 99.9981i | −0.343254 | + | 0.657882i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −226.000 | − | 36.5413i | −1.46753 | − | 0.237281i | ||||
\(155\) | 38.8808 | − | 22.4479i | 0.250844 | − | 0.144825i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.65361 | − | 4.59618i | 0.0169020 | − | 0.0292751i | −0.857451 | − | 0.514566i | \(-0.827953\pi\) |
0.874353 | + | 0.485291i | \(0.161286\pi\) | |||||||
\(158\) | −14.8652 | − | 12.1171i | −0.0940836 | − | 0.0766904i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 23.8098 | − | 83.4598i | 0.148811 | − | 0.521624i | ||||
\(161\) | 244.722 | 1.52001 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 59.5534i | 0.365359i | 0.983173 | + | 0.182679i | \(0.0584770\pi\) | ||||
−0.983173 | + | 0.182679i | \(0.941523\pi\) | |||||||
\(164\) | −34.2211 | − | 166.256i | −0.208665 | − | 1.01376i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −131.791 | − | 107.427i | −0.793924 | − | 0.647152i | ||||
\(167\) | −85.7434 | − | 49.5040i | −0.513434 | − | 0.296431i | 0.220810 | − | 0.975317i | \(-0.429130\pi\) |
−0.734244 | + | 0.678886i | \(0.762463\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 84.3245 | + | 146.054i | 0.498962 | + | 0.864227i | ||||
\(170\) | 47.5490 | + | 7.68808i | 0.279700 | + | 0.0452240i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −46.9248 | + | 141.316i | −0.272819 | + | 0.821605i | ||||
\(173\) | −19.2965 | − | 33.4225i | −0.111540 | − | 0.193193i | 0.804851 | − | 0.593477i | \(-0.202245\pi\) |
−0.916391 | + | 0.400283i | \(0.868912\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −177.201 | − | 102.307i | −1.01258 | − | 0.584612i | ||||
\(176\) | 62.3721 | + | 145.092i | 0.354387 | + | 0.824386i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 46.0436 | + | 121.112i | 0.258672 | + | 0.680405i | ||||
\(179\) | − | 36.4264i | − | 0.203499i | −0.994810 | − | 0.101750i | \(-0.967556\pi\) | ||
0.994810 | − | 0.101750i | \(-0.0324441\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.5921 | −0.102719 | −0.0513594 | − | 0.998680i | \(-0.516355\pi\) | ||||
−0.0513594 | + | 0.998680i | \(0.516355\pi\) | |||||||
\(182\) | 12.8424 | − | 4.88234i | 0.0705626 | − | 0.0268260i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −90.5743 | − | 142.467i | −0.492252 | − | 0.774277i | ||||
\(185\) | 55.1327 | − | 95.4927i | 0.298015 | − | 0.516177i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −75.9055 | + | 43.8240i | −0.405912 | + | 0.234353i | ||||
\(188\) | −2.28716 | + | 6.88788i | −0.0121658 | + | 0.0366377i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12.2069 | + | 75.4968i | −0.0642468 | + | 0.397352i | ||||
\(191\) | −244.973 | + | 141.435i | −1.28258 | + | 0.740497i | −0.977319 | − | 0.211772i | \(-0.932077\pi\) |
−0.305260 | + | 0.952269i | \(0.598743\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −151.542 | + | 262.479i | −0.785193 | + | 1.35999i | 0.143691 | + | 0.989623i | \(0.454103\pi\) |
−0.928884 | + | 0.370372i | \(0.879230\pi\) | |||||||
\(194\) | −9.07644 | + | 11.1350i | −0.0467858 | + | 0.0573967i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 68.9371 | + | 334.917i | 0.351720 | + | 1.70876i | ||||
\(197\) | −139.184 | −0.706520 | −0.353260 | − | 0.935525i | \(-0.614927\pi\) | ||||
−0.353260 | + | 0.935525i | \(0.614927\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.2337i | 0.0564505i | 0.999602 | + | 0.0282253i | \(0.00898558\pi\) | ||||
−0.999602 | + | 0.0282253i | \(0.991014\pi\) | |||||||
\(200\) | 6.02512 | + | 141.024i | 0.0301256 | + | 0.705121i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 140.273 | − | 172.087i | 0.694423 | − | 0.851916i | ||||
\(203\) | 204.404 | + | 118.013i | 1.00692 | + | 0.581344i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −57.5462 | − | 99.6730i | −0.280713 | − | 0.486210i | ||||
\(206\) | −29.3466 | + | 181.502i | −0.142459 | + | 0.881077i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.59541 | − | 5.66930i | −0.0365164 | − | 0.0272563i | ||||
\(209\) | −69.5825 | − | 120.520i | −0.332931 | − | 0.576653i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 112.017 | + | 64.6728i | 0.530884 | + | 0.306506i | 0.741376 | − | 0.671090i | \(-0.234173\pi\) |
−0.210492 | + | 0.977595i | \(0.567507\pi\) | |||||||
\(212\) | −63.0852 | + | 56.0707i | −0.297572 | + | 0.264484i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −201.418 | + | 76.5739i | −0.941207 | + | 0.357822i | ||||
\(215\) | 100.963i | 0.469595i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 191.966 | 0.884634 | ||||||||
\(218\) | −61.5171 | − | 161.813i | −0.282189 | − | 0.742263i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 71.1389 | + | 80.0386i | 0.323359 | + | 0.363812i | ||||
\(221\) | 2.63003 | − | 4.55535i | 0.0119006 | − | 0.0206124i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 209.210 | − | 120.787i | 0.938159 | − | 0.541647i | 0.0487765 | − | 0.998810i | \(-0.484468\pi\) |
0.889383 | + | 0.457163i | \(0.151134\pi\) | |||||||
\(224\) | 266.596 | − | 258.145i | 1.19016 | − | 1.15243i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.28732 | − | 1.50164i | −0.0410943 | − | 0.00664444i | ||||
\(227\) | 330.710 | − | 190.936i | 1.45687 | − | 0.841126i | 0.458016 | − | 0.888944i | \(-0.348560\pi\) |
0.998856 | + | 0.0478181i | \(0.0152268\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 74.6642 | − | 129.322i | 0.326044 | − | 0.564725i | −0.655679 | − | 0.755040i | \(-0.727617\pi\) |
0.981723 | + | 0.190315i | \(0.0609508\pi\) | |||||||
\(230\) | −88.7260 | − | 72.3233i | −0.385765 | − | 0.314449i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.95007 | − | 162.674i | −0.0299572 | − | 0.701180i | ||||
\(233\) | 218.934 | 0.939631 | 0.469816 | − | 0.882765i | \(-0.344320\pi\) | ||||
0.469816 | + | 0.882765i | \(0.344320\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.92103i | 0.0209406i | ||||||||
\(236\) | −346.933 | + | 71.4105i | −1.47006 | + | 0.302587i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 159.636 | + | 130.124i | 0.670738 | + | 0.546739i | ||||
\(239\) | 218.254 | + | 126.009i | 0.913197 | + | 0.527235i | 0.881458 | − | 0.472262i | \(-0.156562\pi\) |
0.0317388 | + | 0.999496i | \(0.489896\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −226.014 | − | 391.467i | −0.937816 | − | 1.62435i | −0.769534 | − | 0.638606i | \(-0.779511\pi\) |
−0.168282 | − | 0.985739i | \(-0.553822\pi\) | |||||||
\(242\) | 46.5366 | + | 7.52439i | 0.192300 | + | 0.0310925i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −277.065 | − | 92.0011i | −1.13551 | − | 0.377053i | ||||
\(245\) | 115.925 | + | 200.787i | 0.473162 | + | 0.819540i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.23284 | + | 4.17588i | 0.0292828 | + | 0.0169064i | ||||
\(248\) | −71.0486 | − | 111.754i | −0.286486 | − | 0.450623i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 82.2006 | + | 216.219i | 0.328802 | + | 0.864874i | ||||
\(251\) | 139.429i | 0.555492i | 0.960655 | + | 0.277746i | \(0.0895874\pi\) | ||||
−0.960655 | + | 0.277746i | \(0.910413\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 208.297 | 0.823306 | ||||||||
\(254\) | 15.6496 | − | 5.94955i | 0.0616125 | − | 0.0234234i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −248.951 | − | 59.6587i | −0.972467 | − | 0.233042i | ||||
\(257\) | −235.308 | + | 407.565i | −0.915594 | + | 1.58586i | −0.109564 | + | 0.993980i | \(0.534946\pi\) |
−0.806029 | + | 0.591875i | \(0.798388\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 408.308 | − | 235.737i | 1.57648 | − | 0.910181i | ||||
\(260\) | −6.09901 | − | 2.02521i | −0.0234577 | − | 0.00778928i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −42.4152 | + | 262.328i | −0.161890 | + | 1.00125i | ||||
\(263\) | 22.2028 | − | 12.8188i | 0.0844214 | − | 0.0487407i | −0.457195 | − | 0.889366i | \(-0.651146\pi\) |
0.541616 | + | 0.840626i | \(0.317813\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −28.6141 | + | 49.5610i | −0.107978 | + | 0.187023i | ||||
\(266\) | −206.607 | + | 253.464i | −0.776717 | + | 0.952874i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −173.318 | + | 35.6746i | −0.646708 | + | 0.133114i | ||||
\(269\) | −8.15075 | −0.0303002 | −0.0151501 | − | 0.999885i | \(-0.504823\pi\) | ||||
−0.0151501 | + | 0.999885i | \(0.504823\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 401.979i | − | 1.48332i | −0.670777 | − | 0.741659i | \(-0.734039\pi\) | ||
0.670777 | − | 0.741659i | \(-0.265961\pi\) | |||||||
\(272\) | 16.6698 | − | 141.094i | 0.0612861 | − | 0.518726i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −57.0102 | + | 69.9400i | −0.208067 | + | 0.255255i | ||||
\(275\) | −150.826 | − | 87.0792i | −0.548457 | − | 0.316652i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 56.2021 | + | 97.3449i | 0.202896 | + | 0.351426i | 0.949460 | − | 0.313887i | \(-0.101631\pi\) |
−0.746565 | + | 0.665313i | \(0.768298\pi\) | |||||||
\(278\) | 48.1939 | − | 298.068i | 0.173359 | − | 1.07219i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 116.394 | − | 223.080i | 0.415691 | − | 0.796716i | ||||
\(281\) | −268.867 | − | 465.692i | −0.956823 | − | 1.65727i | −0.730141 | − | 0.683296i | \(-0.760546\pi\) |
−0.226681 | − | 0.973969i | \(-0.572788\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 122.303 | + | 70.6114i | 0.432164 | + | 0.249510i | 0.700268 | − | 0.713880i | \(-0.253064\pi\) |
−0.268104 | + | 0.963390i | \(0.586397\pi\) | |||||||
\(284\) | −297.083 | − | 334.249i | −1.04607 | − | 1.17693i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.9309 | − | 4.15563i | 0.0382199 | − | 0.0145302i | ||||
\(287\) | − | 492.113i | − | 1.71468i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −210.151 | −0.727167 | ||||||||
\(290\) | −39.2319 | − | 103.195i | −0.135282 | − | 0.355844i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 227.820 | − | 202.489i | 0.780207 | − | 0.693454i | ||||
\(293\) | 230.291 | − | 398.875i | 0.785975 | − | 1.36135i | −0.142440 | − | 0.989803i | \(-0.545495\pi\) |
0.928415 | − | 0.371545i | \(-0.121172\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −207.991 | + | 120.084i | −0.705055 | + | 0.407064i | ||||
\(296\) | −288.356 | − | 150.451i | −0.974175 | − | 0.508282i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 281.904 | + | 45.5804i | 0.945988 | + | 0.152954i | ||||
\(299\) | −10.8258 | + | 6.25029i | −0.0362068 | + | 0.0209040i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −215.849 | + | 373.862i | −0.717107 | + | 1.24206i | ||||
\(302\) | 393.860 | + | 321.047i | 1.30417 | + | 1.06307i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 224.024 | + | 26.4678i | 0.736921 | + | 0.0870653i | ||||
\(305\) | −197.948 | −0.649011 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 210.322i | − | 0.685089i | −0.939502 | − | 0.342545i | \(-0.888711\pi\) | ||
0.939502 | − | 0.342545i | \(-0.111289\pi\) | |||||||
\(308\) | 92.3096 | + | 448.468i | 0.299707 | + | 1.45606i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −69.5987 | − | 56.7320i | −0.224512 | − | 0.183007i | ||||
\(311\) | 110.993 | + | 64.0821i | 0.356892 | + | 0.206052i | 0.667717 | − | 0.744416i | \(-0.267272\pi\) |
−0.310824 | + | 0.950467i | \(0.600605\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.62140 | − | 6.27245i | −0.0115700 | − | 0.0200398i | 0.860182 | − | 0.509986i | \(-0.170350\pi\) |
−0.871752 | + | 0.489947i | \(0.837016\pi\) | |||||||
\(314\) | −10.4784 | − | 1.69422i | −0.0333705 | − | 0.00539560i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.0874 | + | 36.4017i | −0.0382513 | + | 0.115195i | ||||
\(317\) | 120.145 | + | 208.098i | 0.379007 | + | 0.656460i | 0.990918 | − | 0.134467i | \(-0.0429322\pi\) |
−0.611911 | + | 0.790927i | \(0.709599\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 173.980 | + | 100.447i | 0.545392 | + | 0.314882i | ||||
\(320\) | −172.947 | + | 14.8050i | −0.540459 | + | 0.0462656i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −173.928 | − | 457.498i | −0.540151 | − | 1.42080i | ||||
\(323\) | 125.194i | 0.387596i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.4518 | 0.0321595 | ||||||||
\(326\) | 111.333 | − | 42.3258i | 0.341512 | − | 0.129834i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −286.488 | + | 182.137i | −0.873439 | + | 0.555294i | ||||
\(329\) | −10.5207 | + | 18.2224i | −0.0319778 | + | 0.0553872i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −370.385 | + | 213.842i | −1.11899 | + | 0.646048i | −0.941142 | − | 0.338011i | \(-0.890246\pi\) |
−0.177845 | + | 0.984058i | \(0.556913\pi\) | |||||||
\(332\) | −107.164 | + | 322.729i | −0.322784 | + | 0.972076i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −31.6062 | + | 195.477i | −0.0946295 | + | 0.585261i | ||||
\(335\) | −103.906 | + | 59.9904i | −0.310168 | + | 0.179076i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 152.442 | − | 264.037i | 0.452349 | − | 0.783492i | −0.546182 | − | 0.837666i | \(-0.683919\pi\) |
0.998531 | + | 0.0541746i | \(0.0172528\pi\) | |||||||
\(338\) | 213.112 | − | 261.445i | 0.630508 | − | 0.773506i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −19.4214 | − | 94.3550i | −0.0571218 | − | 0.277515i | ||||
\(341\) | 163.393 | 0.479157 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 423.102i | 1.23353i | ||||||||
\(344\) | 297.535 | − | 12.7119i | 0.864927 | − | 0.0369532i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −48.7676 | + | 59.8280i | −0.140947 | + | 0.172913i | ||||
\(347\) | −146.406 | − | 84.5276i | −0.421919 | − | 0.243595i | 0.273979 | − | 0.961736i | \(-0.411660\pi\) |
−0.695898 | + | 0.718140i | \(0.744994\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 107.298 | + | 185.846i | 0.307444 | + | 0.532509i | 0.977802 | − | 0.209529i | \(-0.0671930\pi\) |
−0.670358 | + | 0.742037i | \(0.733860\pi\) | |||||||
\(350\) | −65.3188 | + | 403.982i | −0.186625 | + | 1.15423i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 226.915 | − | 219.722i | 0.644644 | − | 0.624209i | ||||
\(353\) | 275.895 | + | 477.865i | 0.781574 | + | 1.35373i | 0.931025 | + | 0.364956i | \(0.118916\pi\) |
−0.149451 | + | 0.988769i | \(0.547751\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −262.593 | − | 151.608i | −0.739698 | − | 0.427065i | ||||
\(356\) | 193.690 | − | 172.153i | 0.544073 | − | 0.483577i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −68.0977 | + | 25.8889i | −0.190217 | + | 0.0723155i | ||||
\(359\) | 554.828i | 1.54548i | 0.634721 | + | 0.772741i | \(0.281115\pi\) | ||||
−0.634721 | + | 0.772741i | \(0.718885\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 162.222 | 0.449367 | ||||||||
\(362\) | 13.2138 | + | 34.7572i | 0.0365021 | + | 0.0960143i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −18.2547 | − | 20.5384i | −0.0501502 | − | 0.0564241i | ||||
\(365\) | 103.334 | − | 178.980i | 0.283108 | − | 0.490357i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −145.642 | + | 84.0864i | −0.396845 | + | 0.229118i | −0.685122 | − | 0.728429i | \(-0.740251\pi\) |
0.288277 | + | 0.957547i | \(0.406918\pi\) | |||||||
\(368\) | −201.963 | + | 270.579i | −0.548814 | + | 0.735269i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −217.704 | − | 35.2000i | −0.588388 | − | 0.0951350i | ||||
\(371\) | −211.913 | + | 122.348i | −0.571195 | + | 0.329780i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 171.699 | − | 297.391i | 0.460318 | − | 0.797295i | −0.538658 | − | 0.842524i | \(-0.681069\pi\) |
0.998977 | + | 0.0452296i | \(0.0144020\pi\) | |||||||
\(374\) | 135.875 | + | 110.756i | 0.363301 | + | 0.296138i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 14.5021 | − | 0.619590i | 0.0385695 | − | 0.00164785i | ||||
\(377\) | −12.0564 | −0.0319798 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 602.392i | 1.58943i | 0.606986 | + | 0.794713i | \(0.292379\pi\) | ||||
−0.606986 | + | 0.794713i | \(0.707621\pi\) | |||||||
\(380\) | 149.814 | − | 30.8367i | 0.394247 | − | 0.0811493i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 438.514 | + | 357.446i | 1.14794 | + | 0.935722i | ||||
\(383\) | −315.762 | − | 182.305i | −0.824443 | − | 0.475992i | 0.0275035 | − | 0.999622i | \(-0.491244\pi\) |
−0.851946 | + | 0.523630i | \(0.824578\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 155.228 | + | 268.862i | 0.403189 | + | 0.698344i | ||||
\(386\) | 598.398 | + | 96.7534i | 1.55025 | + | 0.250657i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 27.2672 | + | 9.05422i | 0.0702762 | + | 0.0233356i | ||||
\(389\) | −107.326 | − | 185.893i | −0.275901 | − | 0.477875i | 0.694461 | − | 0.719530i | \(-0.255643\pi\) |
−0.970362 | + | 0.241656i | \(0.922310\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −162.280 | − | 93.6923i | −0.415038 | − | 0.239622i | ||||
\(392\) | 577.119 | − | 366.907i | 1.47224 | − | 0.935987i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 98.9209 | + | 260.200i | 0.251068 | + | 0.660405i | ||||
\(395\) | 26.0071i | 0.0658409i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −684.628 | −1.72450 | −0.862251 | − | 0.506480i | \(-0.830946\pi\) | ||||
−0.862251 | + | 0.506480i | \(0.830946\pi\) | |||||||
\(398\) | 21.0009 | − | 7.98397i | 0.0527660 | − | 0.0200602i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 259.357 | − | 111.492i | 0.648392 | − | 0.278731i | ||||
\(401\) | −95.1918 | + | 164.877i | −0.237386 | + | 0.411164i | −0.959963 | − | 0.280125i | \(-0.909624\pi\) |
0.722577 | + | 0.691290i | \(0.242957\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.49203 | + | 4.90287i | −0.0210720 | + | 0.0121659i | ||||
\(404\) | −421.405 | − | 139.930i | −1.04308 | − | 0.346361i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 75.3463 | − | 466.000i | 0.185582 | − | 1.14778i | ||||
\(407\) | 347.534 | − | 200.649i | 0.853892 | − | 0.492995i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 188.978 | − | 327.320i | 0.462049 | − | 0.800293i | −0.537014 | − | 0.843574i | \(-0.680448\pi\) |
0.999063 | + | 0.0432806i | \(0.0137809\pi\) | |||||||
\(410\) | −145.435 | + | 178.420i | −0.354721 | + | 0.435170i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 360.168 | − | 74.1345i | 0.874193 | − | 0.179938i | ||||
\(413\) | −1026.91 | −2.48647 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 230.573i | 0.555598i | ||||||||
\(416\) | −5.20034 | + | 18.2286i | −0.0125008 | + | 0.0438187i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −175.854 | + | 215.738i | −0.420704 | + | 0.516119i | ||||
\(419\) | −267.326 | − | 154.341i | −0.638009 | − | 0.368355i | 0.145838 | − | 0.989308i | \(-0.453412\pi\) |
−0.783847 | + | 0.620954i | \(0.786745\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 176.834 | + | 306.286i | 0.420034 | + | 0.727521i | 0.995942 | − | 0.0899938i | \(-0.0286847\pi\) |
−0.575908 | + | 0.817514i | \(0.695351\pi\) | |||||||
\(422\) | 41.2909 | − | 255.374i | 0.0978457 | − | 0.605153i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 149.658 | + | 78.0848i | 0.352966 | + | 0.184162i | ||||
\(425\) | 78.3369 | + | 135.684i | 0.184322 | + | 0.319255i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −732.995 | − | 423.195i | −1.71662 | − | 0.991088i | ||||
\(428\) | 286.304 | + | 322.121i | 0.668934 | + | 0.752619i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 188.746 | − | 71.7563i | 0.438945 | − | 0.166875i | ||||
\(431\) | − | 472.777i | − | 1.09693i | −0.836174 | − | 0.548465i | \(-0.815213\pi\) | ||
0.836174 | − | 0.548465i | \(-0.184787\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 61.4188 | 0.141845 | 0.0709224 | − | 0.997482i | \(-0.477406\pi\) | ||||
0.0709224 | + | 0.997482i | \(0.477406\pi\) | |||||||
\(434\) | −136.434 | − | 358.872i | −0.314363 | − | 0.826893i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −258.782 | + | 230.007i | −0.593537 | + | 0.527540i | ||||
\(437\) | 148.762 | − | 257.663i | 0.340416 | − | 0.589618i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 354.347 | − | 204.582i | 0.807169 | − | 0.466019i | −0.0388030 | − | 0.999247i | \(-0.512354\pi\) |
0.845972 | + | 0.533228i | \(0.179021\pi\) | |||||||
\(440\) | 99.0691 | − | 189.876i | 0.225157 | − | 0.431537i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.3853 | − | 1.67917i | −0.0234960 | − | 0.00379902i | ||||
\(443\) | −668.806 | + | 386.136i | −1.50972 | + | 0.871638i | −0.509785 | + | 0.860302i | \(0.670275\pi\) |
−0.999936 | + | 0.0113360i | \(0.996392\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 87.8536 | − | 152.167i | 0.197424 | − | 0.341948i | ||||
\(446\) | −374.496 | − | 305.263i | −0.839677 | − | 0.684446i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −672.066 | − | 314.921i | −1.50015 | − | 0.702949i | ||||
\(449\) | 789.037 | 1.75732 | 0.878660 | − | 0.477448i | \(-0.158438\pi\) | ||||
0.878660 | + | 0.477448i | \(0.158438\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 418.865i | − | 0.928747i | ||||||
\(452\) | 3.79341 | + | 18.4295i | 0.00839250 | + | 0.0407733i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −591.988 | − | 482.548i | −1.30394 | − | 1.06288i | ||||
\(455\) | −16.1354 | − | 9.31575i | −0.0354623 | − | 0.0204742i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 138.165 | + | 239.309i | 0.302331 | + | 0.523653i | 0.976664 | − | 0.214775i | \(-0.0689018\pi\) |
−0.674332 | + | 0.738428i | \(0.735568\pi\) | |||||||
\(458\) | −294.828 | − | 47.6700i | −0.643728 | − | 0.104083i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −72.1462 | + | 217.271i | −0.156840 | + | 0.472329i | ||||
\(461\) | 294.041 | + | 509.295i | 0.637834 | + | 1.10476i | 0.985907 | + | 0.167293i | \(0.0535027\pi\) |
−0.348073 | + | 0.937467i | \(0.613164\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 677.285 | + | 391.031i | 1.46282 | + | 0.844558i | 0.999141 | − | 0.0414459i | \(-0.0131964\pi\) |
0.463677 | + | 0.886004i | \(0.346530\pi\) | |||||||
\(464\) | −299.172 | + | 128.608i | −0.644768 | + | 0.277173i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −155.601 | − | 409.288i | −0.333907 | − | 0.878301i | ||||
\(467\) | − | 663.203i | − | 1.42014i | −0.704133 | − | 0.710068i | \(-0.748664\pi\) | ||
0.704133 | − | 0.710068i | \(-0.251336\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −513.014 | −1.09385 | ||||||||
\(470\) | 9.19967 | − | 3.49747i | 0.0195738 | − | 0.00744143i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 380.071 | + | 597.825i | 0.805235 | + | 1.26658i | ||||
\(473\) | −183.721 | + | 318.214i | −0.388417 | + | 0.672758i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −215.434 | + | 124.381i | −0.453546 | + | 0.261855i | ||||
\(476\) | 129.805 | − | 390.914i | 0.272700 | − | 0.821247i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 80.4516 | − | 497.574i | 0.168309 | − | 1.04095i | ||||
\(479\) | 562.018 | − | 324.481i | 1.17331 | − | 0.677414i | 0.218856 | − | 0.975757i | \(-0.429767\pi\) |
0.954459 | + | 0.298344i | \(0.0964341\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.0416 | + | 20.8567i | −0.0250346 | + | 0.0433611i | ||||
\(482\) | −571.200 | + | 700.746i | −1.18506 | + | 1.45383i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −19.0079 | − | 92.3460i | −0.0392725 | − | 0.190798i | ||||
\(485\) | 19.4810 | 0.0401669 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 282.104i | − | 0.579269i | −0.957137 | − | 0.289635i | \(-0.906466\pi\) | ||
0.957137 | − | 0.289635i | \(-0.0935338\pi\) | |||||||
\(488\) | 24.9230 | + | 583.348i | 0.0510717 | + | 1.19539i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 292.974 | − | 359.420i | 0.597906 | − | 0.733510i | ||||
\(491\) | 652.933 | + | 376.971i | 1.32980 | + | 0.767762i | 0.985269 | − | 0.171012i | \(-0.0547036\pi\) |
0.344534 | + | 0.938774i | \(0.388037\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −90.3630 | − | 156.513i | −0.183292 | − | 0.317471i | ||||
\(494\) | 2.66613 | − | 16.4894i | 0.00539702 | − | 0.0333793i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −158.425 | + | 212.248i | −0.319405 | + | 0.427920i | ||||
\(497\) | −648.247 | − | 1122.80i | −1.30432 | − | 2.25915i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 446.169 | + | 257.596i | 0.894126 | + | 0.516224i | 0.875290 | − | 0.483599i | \(-0.160671\pi\) |
0.0188362 | + | 0.999823i | \(0.494004\pi\) | |||||||
\(500\) | 345.790 | − | 307.341i | 0.691581 | − | 0.614682i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 260.656 | − | 99.0945i | 0.519235 | − | 0.197399i | ||||
\(503\) | 523.660i | 1.04107i | 0.853839 | + | 0.520537i | \(0.174268\pi\) | ||||
−0.853839 | + | 0.520537i | \(0.825732\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −301.072 | −0.596182 | ||||||||
\(506\) | −148.040 | − | 389.402i | −0.292570 | − | 0.769569i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −22.2449 | − | 25.0278i | −0.0437892 | − | 0.0492673i | ||||
\(509\) | 267.685 | − | 463.645i | 0.525905 | − | 0.910893i | −0.473640 | − | 0.880719i | \(-0.657060\pi\) |
0.999545 | − | 0.0301749i | \(-0.00960643\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 765.285 | − | 441.838i | 1.49762 | − | 0.864653i | ||||
\(512\) | 65.4050 | + | 507.805i | 0.127744 | + | 0.991807i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 929.163 | + | 150.234i | 1.80771 | + | 0.292284i | ||||
\(515\) | 215.925 | − | 124.665i | 0.419273 | − | 0.242067i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.95475 | + | 15.5101i | −0.0173206 | + | 0.0300002i | ||||
\(518\) | −730.893 | − | 595.773i | −1.41099 | − | 1.15014i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.548628 | + | 12.8412i | 0.00105505 | + | 0.0246946i | ||||
\(521\) | −177.268 | −0.340246 | −0.170123 | − | 0.985423i | \(-0.554416\pi\) | ||||
−0.170123 | + | 0.985423i | \(0.554416\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 444.206i | − | 0.849343i | −0.905347 | − | 0.424672i | \(-0.860390\pi\) | ||
0.905347 | − | 0.424672i | \(-0.139610\pi\) | |||||||
\(524\) | 520.558 | − | 107.148i | 0.993431 | − | 0.204481i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −39.7442 | − | 32.3967i | −0.0755593 | − | 0.0615907i | ||||
\(527\) | −127.296 | − | 73.4944i | −0.241548 | − | 0.139458i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −41.8394 | − | 72.4679i | −0.0790914 | − | 0.136990i | ||||
\(530\) | 112.989 | + | 18.2689i | 0.213187 | + | 0.0344696i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 620.681 | + | 206.101i | 1.16669 | + | 0.387407i | ||||
\(533\) | 12.5688 | + | 21.7697i | 0.0235812 | + | 0.0408438i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 253.065 | + | 146.107i | 0.473018 | + | 0.273097i | ||||
\(536\) | 189.872 | + | 298.656i | 0.354239 | + | 0.557194i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.79289 | + | 15.2375i | 0.0107675 | + | 0.0283225i | ||||
\(539\) | 843.787i | 1.56547i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 571.163 | 1.05575 | 0.527877 | − | 0.849321i | \(-0.322988\pi\) | ||||
0.527877 | + | 0.849321i | \(0.322988\pi\) | |||||||
\(542\) | −751.484 | + | 285.694i | −1.38650 | + | 0.527111i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −275.616 | + | 69.1142i | −0.506647 | + | 0.127048i | ||||
\(545\) | −117.378 | + | 203.304i | −0.215372 | + | 0.373036i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −139.875 | + | 80.7569i | −0.255713 | + | 0.147636i | −0.622377 | − | 0.782717i | \(-0.713833\pi\) |
0.366664 | + | 0.930353i | \(0.380500\pi\) | |||||||
\(548\) | 171.268 | + | 56.8706i | 0.312533 | + | 0.103779i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −55.5965 | + | 343.851i | −0.101085 | + | 0.625184i | ||||
\(551\) | 248.507 | − | 143.476i | 0.451011 | − | 0.260391i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −55.6008 | + | 96.3034i | −0.100544 | + | 0.174147i | ||||
\(554\) | 142.038 | − | 174.252i | 0.256387 | − | 0.314535i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −591.479 | + | 121.746i | −1.06381 | + | 0.218968i | ||||
\(557\) | 568.917 | 1.02139 | 0.510697 | − | 0.859761i | \(-0.329387\pi\) | ||||
0.510697 | + | 0.859761i | \(0.329387\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 22.0515i | − | 0.0394481i | ||||||
\(560\) | −499.763 | − | 59.0457i | −0.892434 | − | 0.105439i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −679.503 | + | 833.612i | −1.20908 | + | 1.48330i | ||||
\(563\) | 250.527 | + | 144.642i | 0.444985 | + | 0.256912i | 0.705710 | − | 0.708501i | \(-0.250628\pi\) |
−0.260725 | + | 0.965413i | \(0.583962\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.37900 | + | 11.0487i | 0.0112903 | + | 0.0195553i | ||||
\(566\) | 45.0824 | − | 278.824i | 0.0796510 | − | 0.492623i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −413.723 | + | 792.942i | −0.728385 | + | 1.39603i | ||||
\(569\) | 223.117 | + | 386.450i | 0.392121 | + | 0.679174i | 0.992729 | − | 0.120370i | \(-0.0384079\pi\) |
−0.600608 | + | 0.799544i | \(0.705075\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −372.386 | − | 214.997i | −0.652164 | − | 0.376527i | 0.137121 | − | 0.990554i | \(-0.456215\pi\) |
−0.789285 | + | 0.614027i | \(0.789549\pi\) | |||||||
\(572\) | −15.5376 | − | 17.4813i | −0.0271636 | − | 0.0305618i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −919.986 | + | 349.754i | −1.60276 | + | 0.609328i | ||||
\(575\) | − | 372.337i | − | 0.647542i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 50.9694 | 0.0883353 | 0.0441676 | − | 0.999024i | \(-0.485936\pi\) | ||||
0.0441676 | + | 0.999024i | \(0.485936\pi\) | |||||||
\(578\) | 149.359 | + | 392.869i | 0.258406 | + | 0.679705i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −165.035 | + | 146.685i | −0.284544 | + | 0.252905i | ||||
\(581\) | −492.943 | + | 853.803i | −0.848440 | + | 1.46954i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −180.371 | + | 104.137i | −0.309385 | + | 0.178623i | ||||
\(584\) | −540.460 | − | 281.989i | −0.925446 | − | 0.482857i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −909.353 | − | 147.031i | −1.55180 | − | 0.250906i | ||||
\(587\) | −643.771 | + | 371.681i | −1.09671 | + | 0.633188i | −0.935356 | − | 0.353708i | \(-0.884921\pi\) |
−0.161358 | + | 0.986896i | \(0.551587\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 116.692 | − | 202.117i | 0.198119 | − | 0.343152i | ||||
\(590\) | 372.315 | + | 303.485i | 0.631042 | + | 0.514382i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −76.3230 | + | 645.998i | −0.128924 | + | 1.09121i | ||||
\(593\) | 382.547 | 0.645104 | 0.322552 | − | 0.946552i | \(-0.395459\pi\) | ||||
0.322552 | + | 0.946552i | \(0.395459\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 279.287i | − | 0.469391i | ||||||
\(596\) | −115.144 | − | 559.404i | −0.193195 | − | 0.938597i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 19.3788 | + | 15.7962i | 0.0324060 | + | 0.0264151i | ||||
\(599\) | 856.248 | + | 494.355i | 1.42946 | + | 0.825301i | 0.997078 | − | 0.0763888i | \(-0.0243390\pi\) |
0.432384 | + | 0.901689i | \(0.357672\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −263.280 | − | 456.015i | −0.438070 | − | 0.758760i | 0.559470 | − | 0.828850i | \(-0.311005\pi\) |
−0.997541 | + | 0.0700905i | \(0.977671\pi\) | |||||||
\(602\) | 852.327 | + | 137.811i | 1.41583 | + | 0.228921i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 320.261 | − | 964.479i | 0.530233 | − | 1.59682i | ||||
\(605\) | −31.9637 | − | 55.3627i | −0.0528325 | − | 0.0915086i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −447.631 | − | 258.440i | −0.737448 | − | 0.425766i | 0.0836928 | − | 0.996492i | \(-0.473329\pi\) |
−0.821141 | + | 0.570726i | \(0.806662\pi\) | |||||||
\(608\) | −109.737 | − | 437.615i | −0.180489 | − | 0.719761i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 140.686 | + | 370.057i | 0.230632 | + | 0.606650i | ||||
\(611\) | − | 1.07481i | − | 0.00175910i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 762.957 | 1.24463 | 0.622314 | − | 0.782768i | \(-0.286193\pi\) | ||||
0.622314 | + | 0.782768i | \(0.286193\pi\) | |||||||
\(614\) | −393.189 | + | 149.480i | −0.640373 | + | 0.243453i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 772.786 | − | 491.303i | 1.25452 | − | 0.797571i | ||||
\(617\) | −60.9168 | + | 105.511i | −0.0987307 | + | 0.171007i | −0.911160 | − | 0.412054i | \(-0.864812\pi\) |
0.812429 | + | 0.583060i | \(0.198145\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −265.675 | + | 153.388i | −0.429200 | + | 0.247799i | −0.699006 | − | 0.715116i | \(-0.746374\pi\) |
0.269806 | + | 0.962915i | \(0.413041\pi\) | |||||||
\(620\) | −56.5931 | + | 170.433i | −0.0912793 | + | 0.274891i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 40.9138 | − | 253.042i | 0.0657778 | − | 0.406820i | ||||
\(623\) | 650.636 | − | 375.645i | 1.04436 | − | 0.602961i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −63.7082 | + | 110.346i | −0.101933 | + | 0.176553i | ||||
\(626\) | −9.15230 | + | 11.2280i | −0.0146203 | + | 0.0179361i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.27989 | + | 20.7930i | 0.00681511 | + | 0.0331098i | ||||
\(629\) | −361.010 | −0.573942 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1071.11i | 1.69749i | 0.528805 | + | 0.848744i | \(0.322640\pi\) | ||||
−0.528805 | + | 0.848744i | \(0.677360\pi\) | |||||||
\(632\) | 76.6423 | − | 3.27447i | 0.121269 | − | 0.00518112i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 303.641 | − | 372.506i | 0.478929 | − | 0.587549i | ||||
\(635\) | −19.6623 | − | 11.3521i | −0.0309643 | − | 0.0178773i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −25.3193 | − | 43.8543i | −0.0397477 | − | 0.0688450i | ||||
\(638\) | 64.1315 | − | 396.638i | 0.100520 | − | 0.621690i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 150.594 | + | 312.795i | 0.235303 | + | 0.488742i | ||||
\(641\) | −527.259 | − | 913.240i | −0.822557 | − | 1.42471i | −0.903772 | − | 0.428015i | \(-0.859213\pi\) |
0.0812143 | − | 0.996697i | \(-0.474120\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 42.0680 | + | 24.2880i | 0.0654246 | + | 0.0377729i | 0.532355 | − | 0.846521i | \(-0.321307\pi\) |
−0.466931 | + | 0.884294i | \(0.654640\pi\) | |||||||
\(644\) | −731.659 | + | 650.305i | −1.13612 | + | 1.00979i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 234.044 | − | 88.9774i | 0.362298 | − | 0.137736i | ||||
\(647\) | − | 539.373i | − | 0.833653i | −0.908986 | − | 0.416826i | \(-0.863142\pi\) | ||
0.908986 | − | 0.416826i | \(-0.136858\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −874.061 | −1.34678 | ||||||||
\(650\) | −7.42832 | − | 19.5393i | −0.0114282 | − | 0.0300605i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −158.253 | − | 178.050i | −0.242719 | − | 0.273083i | ||||
\(653\) | 276.457 | − | 478.838i | 0.423365 | − | 0.733290i | −0.572901 | − | 0.819624i | \(-0.694182\pi\) |
0.996266 | + | 0.0863348i | \(0.0275155\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 312.081 | − | 180.180i | 0.476460 | − | 0.275084i | ||||
\(656\) | 544.109 | + | 406.130i | 0.829435 | + | 0.619100i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 41.5433 | + | 6.71703i | 0.0631357 | + | 0.0102082i | ||||
\(659\) | −734.162 | + | 423.869i | −1.11406 | + | 0.643200i | −0.939877 | − | 0.341514i | \(-0.889060\pi\) |
−0.174178 | + | 0.984714i | \(0.555727\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −359.447 | + | 622.580i | −0.543792 | + | 0.941876i | 0.454890 | + | 0.890548i | \(0.349679\pi\) |
−0.998682 | + | 0.0513280i | \(0.983655\pi\) | |||||||
\(662\) | 663.008 | + | 540.438i | 1.00152 | + | 0.816372i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 679.493 | − | 29.0307i | 1.02333 | − | 0.0437209i | ||||
\(665\) | 443.444 | 0.666833 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 429.497i | 0.643923i | ||||||||
\(668\) | 387.900 | − | 79.8428i | 0.580689 | − | 0.119525i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 185.998 | + | 151.612i | 0.277609 | + | 0.226287i | ||||
\(671\) | −623.893 | − | 360.205i | −0.929796 | − | 0.536818i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 288.488 | + | 499.675i | 0.428659 | + | 0.742460i | 0.996754 | − | 0.0805033i | \(-0.0256528\pi\) |
−0.568095 | + | 0.822963i | \(0.692319\pi\) | |||||||
\(674\) | −601.949 | − | 97.3277i | −0.893100 | − | 0.144403i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −640.223 | − | 212.590i | −0.947076 | − | 0.314482i | ||||
\(677\) | 101.021 | + | 174.974i | 0.149219 | + | 0.258454i | 0.930939 | − | 0.365175i | \(-0.118991\pi\) |
−0.781720 | + | 0.623629i | \(0.785657\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 72.1372 | + | 41.6484i | 0.106240 | + | 0.0613379i | ||||
\(680\) | −162.590 | + | 103.367i | −0.239102 | + | 0.152011i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −116.126 | − | 305.456i | −0.170273 | − | 0.447882i | ||||
\(683\) | 568.249i | 0.831990i | 0.909367 | + | 0.415995i | \(0.136567\pi\) | ||||
−0.909367 | + | 0.415995i | \(0.863433\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 122.362 | 0.178631 | ||||||||
\(686\) | 790.972 | − | 300.707i | 1.15302 | − | 0.438348i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −235.228 | − | 547.195i | −0.341901 | − | 0.795341i | ||||
\(689\) | 6.24965 | − | 10.8247i | 0.00907060 | − | 0.0157107i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 351.376 | − | 202.867i | 0.508504 | − | 0.293585i | −0.223714 | − | 0.974655i | \(-0.571818\pi\) |
0.732218 | + | 0.681070i | \(0.238485\pi\) | |||||||
\(692\) | 146.506 | + | 48.6482i | 0.211714 | + | 0.0703008i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −53.9673 | + | 333.775i | −0.0777627 | + | 0.480945i | ||||
\(695\) | −354.600 | + | 204.728i | −0.510215 | + | 0.294573i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −188.407 | + | 326.330i | −0.270311 | + | 0.468192i | ||||
\(698\) | 271.172 | − | 332.673i | 0.388499 | − | 0.476609i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 801.651 | − | 165.007i | 1.14522 | − | 0.235724i | ||||
\(701\) | −83.5164 | −0.119139 | −0.0595695 | − | 0.998224i | \(-0.518973\pi\) | ||||
−0.0595695 | + | 0.998224i | \(0.518973\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 573.200i | − | 0.815363i | ||||||
\(704\) | −572.033 | − | 268.047i | −0.812547 | − | 0.380749i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 697.265 | − | 855.403i | 0.987628 | − | 1.21162i | ||||
\(707\) | −1114.86 | − | 643.663i | −1.57688 | − | 0.910414i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −173.908 | − | 301.217i | −0.245286 | − | 0.424848i | 0.716926 | − | 0.697149i | \(-0.245548\pi\) |
−0.962212 | + | 0.272302i | \(0.912215\pi\) | |||||||
\(710\) | −96.7955 | + | 598.657i | −0.136332 | + | 0.843180i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −459.493 | − | 239.743i | −0.645355 | − | 0.336718i | ||||
\(713\) | 174.660 | + | 302.520i | 0.244965 | + | 0.424292i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.7337 | − | 7.92916i | −0.0192080 | − | 0.0110897i | ||||
\(716\) | 96.7966 | + | 108.906i | 0.135191 | + | 0.152104i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1037.23 | − | 394.327i | 1.44461 | − | 0.549202i | ||||
\(719\) | − | 536.277i | − | 0.745865i | −0.927858 | − | 0.372933i | \(-0.878352\pi\) | ||
0.927858 | − | 0.372933i | \(-0.121648\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1066.08 | 1.47862 | ||||||||
\(722\) | −115.294 | − | 303.267i | −0.159687 | − | 0.420037i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 55.5859 | − | 49.4052i | 0.0767761 | − | 0.0682392i | ||||
\(725\) | 179.553 | − | 310.995i | 0.247659 | − | 0.428959i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −815.055 | + | 470.573i | −1.12112 | + | 0.647280i | −0.941687 | − | 0.336490i | \(-0.890760\pi\) |
−0.179435 | + | 0.983770i | \(0.557427\pi\) | |||||||
\(728\) | −25.4217 | + | 48.7233i | −0.0349199 | + | 0.0669277i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −408.038 | − | 65.9747i | −0.558956 | − | 0.0903763i | ||||
\(731\) | 286.267 | − | 165.277i | 0.391611 | − | 0.226096i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 311.063 | − | 538.777i | 0.424370 | − | 0.735030i | −0.571991 | − | 0.820260i | \(-0.693829\pi\) |
0.996361 | + | 0.0852294i | \(0.0271623\pi\) | |||||||
\(734\) | 260.707 | + | 212.510i | 0.355186 | + | 0.289523i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 649.376 | + | 185.257i | 0.882304 | + | 0.251708i | ||||
\(737\) | −436.655 | −0.592477 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 444.439i | − | 0.601406i | −0.953718 | − | 0.300703i | \(-0.902779\pi\) | ||
0.953718 | − | 0.300703i | \(-0.0972213\pi\) | |||||||
\(740\) | 88.9212 | + | 432.005i | 0.120164 | + | 0.583791i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 379.336 | + | 309.208i | 0.511235 | + | 0.416723i | ||||
\(743\) | −66.2270 | − | 38.2362i | −0.0891346 | − | 0.0514619i | 0.454770 | − | 0.890609i | \(-0.349721\pi\) |
−0.543905 | + | 0.839147i | \(0.683055\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −193.626 | − | 335.370i | −0.259901 | − | 0.450161i | ||||
\(746\) | −677.990 | − | 109.622i | −0.908833 | − | 0.146947i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 110.484 | − | 332.728i | 0.147706 | − | 0.444824i | ||||
\(749\) | 624.725 | + | 1082.06i | 0.834079 | + | 1.44467i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 949.025 | + | 547.920i | 1.26368 | + | 0.729587i | 0.973785 | − | 0.227471i | \(-0.0730457\pi\) |
0.289897 | + | 0.957058i | \(0.406379\pi\) | |||||||
\(752\) | −11.4652 | − | 26.6708i | −0.0152463 | − | 0.0354665i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.56870 | + | 22.5389i | 0.0113643 | + | 0.0298925i | ||||
\(755\) | − | 689.070i | − | 0.912676i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −346.346 | −0.457525 | −0.228762 | − | 0.973482i | \(-0.573468\pi\) | ||||
−0.228762 | + | 0.973482i | \(0.573468\pi\) | |||||||
\(758\) | 1126.15 | − | 428.132i | 1.48568 | − | 0.564817i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −164.124 | − | 258.155i | −0.215952 | − | 0.339677i | ||||
\(761\) | 106.565 | − | 184.576i | 0.140033 | − | 0.242544i | −0.787476 | − | 0.616345i | \(-0.788613\pi\) |
0.927509 | + | 0.373802i | \(0.121946\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −869.291 | + | 501.885i | −1.13931 | + | 0.657779i | ||||
\(764\) | 356.571 | − | 1073.83i | 0.466715 | − | 1.40553i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −116.394 | + | 719.871i | −0.151951 | + | 0.939779i | ||||
\(767\) | 45.4277 | − | 26.2277i | 0.0592277 | − | 0.0341952i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −270.786 | + | 469.015i | −0.352127 | + | 0.609902i | −0.986622 | − | 0.163025i | \(-0.947875\pi\) |
0.634495 | + | 0.772927i | \(0.281208\pi\) | |||||||
\(770\) | 392.304 | − | 481.278i | 0.509486 | − | 0.625036i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −244.416 | − | 1187.44i | −0.316601 | − | 1.53814i | ||||
\(773\) | −1255.73 | −1.62449 | −0.812245 | − | 0.583317i | \(-0.801755\pi\) | ||||
−0.812245 | + | 0.583317i | \(0.801755\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 292.070i | − | 0.376864i | ||||||
\(776\) | −2.45278 | − | 57.4098i | −0.00316080 | − | 0.0739818i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −271.242 | + | 332.759i | −0.348640 | + | 0.427710i | ||||
\(779\) | −518.136 | − | 299.146i | −0.665130 | − | 0.384013i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −551.759 | − | 955.675i | −0.706478 | − | 1.22366i | ||||
\(782\) | −59.8186 | + | 369.964i | −0.0764944 | + | 0.473100i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1096.09 | − | 818.133i | −1.39807 | − | 1.04354i | ||||
\(785\) | 7.19706 | + | 12.4657i | 0.00916822 | + | 0.0158798i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −859.448 | − | 496.202i | −1.09206 | − | 0.630499i | −0.157933 | − | 0.987450i | \(-0.550483\pi\) |
−0.934123 | + | 0.356951i | \(0.883816\pi\) | |||||||
\(788\) | 416.127 | − | 369.857i | 0.528081 | − | 0.469362i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 48.6193 | − | 18.4838i | 0.0615434 | − | 0.0233972i | ||||
\(791\) | 54.5507i | 0.0689643i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 43.2342 | 0.0545198 | ||||||||
\(794\) | 486.578 | + | 1279.88i | 0.612818 | + | 1.61194i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −29.8514 | − | 33.5859i | −0.0375018 | − | 0.0421934i | ||||
\(797\) | −319.262 | + | 552.978i | −0.400580 | + | 0.693824i | −0.993796 | − | 0.111219i | \(-0.964525\pi\) |
0.593216 | + | 0.805043i | \(0.297858\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.9530 | − | 8.05574i | 0.0174630 | − | 0.0100823i | ||||
\(800\) | −392.760 | − | 405.617i | −0.490950 | − | 0.507022i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 375.885 | + | 60.7760i | 0.468685 | + | 0.0757805i | ||||
\(803\) | 651.377 | − | 376.073i | 0.811179 | − | 0.468335i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −331.865 | + | 574.806i | −0.412254 | + | 0.714045i | ||||
\(806\) | 15.2012 | + | 12.3909i | 0.0188600 | + | 0.0153734i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 37.9069 | + | 887.250i | 0.0469145 | + | 1.09808i | ||||
\(809\) | 174.260 | 0.215401 | 0.107701 | − | 0.994183i | \(-0.465651\pi\) | ||||
0.107701 | + | 0.994183i | \(0.465651\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1182.19i | 1.45770i | 0.684675 | + | 0.728849i | \(0.259944\pi\) | ||||
−0.684675 | + | 0.728849i | \(0.740056\pi\) | |||||||
\(812\) | −924.717 | + | 190.338i | −1.13881 | + | 0.234406i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −622.104 | − | 507.096i | −0.764256 | − | 0.622968i | ||||
\(815\) | −139.880 | − | 80.7597i | −0.171632 | − | 0.0990917i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 262.421 | + | 454.527i | 0.321201 | + | 0.556336i | ||||
\(818\) | −746.222 | − | 120.655i | −0.912251 | − | 0.147500i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 436.912 | + | 145.079i | 0.532820 | + | 0.176926i | ||||
\(821\) | −293.955 | − | 509.144i | −0.358045 | − | 0.620151i | 0.629590 | − | 0.776928i | \(-0.283223\pi\) |
−0.987634 | + | 0.156777i | \(0.949890\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −98.0750 | − | 56.6236i | −0.119168 | − | 0.0688015i | 0.439231 | − | 0.898374i | \(-0.355251\pi\) |
−0.558399 | + | 0.829573i | \(0.688584\pi\) | |||||||
\(824\) | −394.569 | − | 620.630i | −0.478846 | − | 0.753192i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 729.844 | + | 1919.77i | 0.883589 | + | 2.32417i | ||||
\(827\) | 800.560i | 0.968030i | 0.875060 | + | 0.484015i | \(0.160822\pi\) | ||||
−0.875060 | + | 0.484015i | \(0.839178\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1162.87 | 1.40274 | 0.701369 | − | 0.712798i | \(-0.252573\pi\) | ||||
0.701369 | + | 0.712798i | \(0.252573\pi\) | |||||||
\(830\) | 431.047 | − | 163.873i | 0.519334 | − | 0.197437i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 37.7736 | − | 3.23358i | 0.0454009 | − | 0.00388652i | ||||
\(833\) | 379.538 | − | 657.378i | 0.455627 | − | 0.789170i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 232.551 | − | 134.264i | 0.278505 | − | 0.160795i | ||||
\(836\) | 528.296 | + | 175.424i | 0.631933 | + | 0.209837i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −98.5400 | + | 609.447i | −0.117590 | + | 0.727264i | ||||
\(839\) | −1355.92 | + | 782.842i | −1.61612 | + | 0.933065i | −0.628205 | + | 0.778048i | \(0.716210\pi\) |
−0.987912 | + | 0.155017i | \(0.950457\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 213.383 | − | 369.590i | 0.253725 | − | 0.439464i | ||||
\(842\) | 446.910 | − | 548.268i | 0.530772 | − | 0.651150i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −506.758 | + | 104.308i | −0.600425 | + | 0.123587i | ||||
\(845\) | −457.406 | −0.541309 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 273.341i | − | 0.322717i | ||||||
\(848\) | 39.6119 | − | 335.275i | 0.0467121 | − | 0.395372i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 197.979 | − | 242.881i | 0.232917 | − | 0.285742i | ||||
\(851\) | 743.000 | + | 428.971i | 0.873091 | + | 0.504079i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −68.8088 | − | 119.180i | −0.0806668 | − | 0.139719i | 0.822870 | − | 0.568230i | \(-0.192372\pi\) |
−0.903537 | + | 0.428511i | \(0.859038\pi\) | |||||||
\(854\) | −270.192 | + | 1671.08i | −0.316384 | + | 1.95676i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 398.711 | − | 764.170i | 0.465783 | − | 0.892722i | ||||
\(857\) | 384.489 | + | 665.955i | 0.448646 | + | 0.777077i | 0.998298 | − | 0.0583164i | \(-0.0185732\pi\) |
−0.549653 | + | 0.835393i | \(0.685240\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −178.353 | − | 102.972i | −0.207629 | − | 0.119875i | 0.392580 | − | 0.919718i | \(-0.371583\pi\) |
−0.600209 | + | 0.799843i | \(0.704916\pi\) | |||||||
\(860\) | −268.291 | − | 301.855i | −0.311966 | − | 0.350994i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −883.837 | + | 336.011i | −1.02533 | + | 0.389804i | ||||
\(863\) | 772.757i | 0.895431i | 0.894176 | + | 0.447716i | \(0.147762\pi\) | ||||
−0.894176 | + | 0.447716i | \(0.852238\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 104.671 | 0.121007 | ||||||||
\(866\) | −43.6515 | − | 114.820i | −0.0504059 | − | 0.132587i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −573.930 | + | 510.114i | −0.661210 | + | 0.587689i | ||||
\(869\) | −47.3249 | + | 81.9692i | −0.0544591 | + | 0.0943258i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.6943 | − | 13.1026i | 0.0260555 | − | 0.0150432i | ||||
\(872\) | 613.911 | + | 320.312i | 0.704026 | + | 0.367330i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −587.418 | − | 94.9782i | −0.672103 | − | 0.108671i | ||||
\(875\) | 1161.57 | − | 670.630i | 1.32750 | − | 0.766435i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −200.096 | + | 346.577i | −0.228160 | + | 0.395185i | −0.957263 | − | 0.289219i | \(-0.906604\pi\) |
0.729103 | + | 0.684404i | \(0.239938\pi\) | |||||||
\(878\) | −634.300 | − | 517.037i | −0.722437 | − | 0.588880i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −425.376 | − | 50.2571i | −0.483382 | − | 0.0571103i | ||||
\(881\) | 728.323 | 0.826700 | 0.413350 | − | 0.910572i | \(-0.364359\pi\) | ||||
0.413350 | + | 0.910572i | \(0.364359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 383.413i | − | 0.434216i | −0.976148 | − | 0.217108i | \(-0.930338\pi\) | ||
0.976148 | − | 0.217108i | \(-0.0696625\pi\) | |||||||
\(884\) | 4.24186 | + | 20.6082i | 0.00479848 | + | 0.0233125i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1197.20 | + | 975.873i | 1.35124 | + | 1.10144i | ||||
\(887\) | 1255.91 | + | 725.098i | 1.41590 | + | 0.817473i | 0.995936 | − | 0.0900662i | \(-0.0287079\pi\) |
0.419968 | + | 0.907539i | \(0.362041\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −48.5392 | − | 84.0724i | −0.0545998 | − | 0.0945696i | ||||
\(890\) | −346.909 | − | 56.0909i | −0.389785 | − | 0.0630234i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −304.516 | + | 917.061i | −0.341385 | + | 1.02810i | ||||
\(893\) | 12.7907 | + | 22.1541i | 0.0143232 | + | 0.0248086i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 85.5589 | + | 49.3974i | 0.0955965 | + | 0.0551927i | ||||
\(896\) | −111.082 | + | 1480.22i | −0.123976 | + | 1.65203i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −560.783 | − | 1475.07i | −0.624480 | − | 1.64262i | ||||
\(899\) | 336.907i | 0.374758i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 187.365 | 0.207952 | ||||||||
\(902\) | −783.051 | + | 297.695i | −0.868128 | + | 0.330039i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 31.7572 | − | 20.1898i | 0.0351296 | − | 0.0223339i | ||||
\(905\) | 25.2125 | − | 43.6694i | 0.0278592 | − | 0.0482535i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 533.290 | − | 307.895i | 0.587971 | − | 0.339465i | −0.176324 | − | 0.984332i | \(-0.556420\pi\) |
0.764295 | + | 0.644867i | \(0.223087\pi\) | |||||||
\(908\) | −481.366 | + | 1449.65i | −0.530139 | + | 1.59653i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.94772 | + | 36.7853i | −0.00653596 | + | 0.0404234i | ||||
\(911\) | 227.031 | − | 131.076i | 0.249211 | − | 0.143882i | −0.370192 | − | 0.928955i | \(-0.620708\pi\) |
0.619403 | + | 0.785073i | \(0.287375\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −419.572 | + | 726.720i | −0.459553 | + | 0.795969i | ||||
\(914\) | 349.183 | − | 428.376i | 0.382038 | − | 0.468683i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 120.423 | + | 585.048i | 0.131466 | + | 0.638699i | ||||
\(917\) | 1540.83 | 1.68030 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 566.458i | 0.616385i | 0.951324 | + | 0.308193i | \(0.0997241\pi\) | ||||
−0.951324 | + | 0.308193i | \(0.900276\pi\) | |||||||
\(920\) | 457.455 | − | 19.5443i | 0.497234 | − | 0.0212438i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 743.125 | − | 911.664i | 0.805992 | − | 0.988789i | ||||
\(923\) | 57.3533 | + | 33.1130i | 0.0621379 | + | 0.0358754i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −358.667 | − | 621.229i | −0.387748 | − | 0.671599i | ||||
\(926\) | 249.657 | − | 1544.07i | 0.269608 | − | 1.66746i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 453.055 | + | 467.886i | 0.488206 | + | 0.504188i | ||||
\(929\) | −298.745 | − | 517.442i | −0.321577 | − | 0.556988i | 0.659236 | − | 0.751936i | \(-0.270880\pi\) |
−0.980814 | + | 0.194948i | \(0.937546\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1043.77 | + | 602.618i | 1.12112 | + | 0.647281i | ||||
\(932\) | −654.560 | + | 581.778i | −0.702317 | + | 0.624225i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1239.83 | + | 471.351i | −1.32744 | + | 0.504659i | ||||
\(935\) | − | 237.717i | − | 0.254243i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 457.785 | 0.488564 | 0.244282 | − | 0.969704i | \(-0.421448\pi\) | ||||
0.244282 | + | 0.969704i | \(0.421448\pi\) | |||||||
\(938\) | 364.609 | + | 959.060i | 0.388709 | + | 1.02245i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −13.0768 | − | 14.7127i | −0.0139114 | − | 0.0156518i | ||||
\(941\) | 677.858 | − | 1174.09i | 0.720360 | − | 1.24770i | −0.240496 | − | 0.970650i | \(-0.577310\pi\) |
0.960856 | − | 0.277049i | \(-0.0893566\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 775.526 | − | 447.750i | 0.822403 | − | 0.474814i | ||||
\(944\) | 847.486 | − | 1135.41i | 0.897760 | − | 1.20277i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 725.463 | + | 117.298i | 0.766874 | + | 0.123994i | ||||
\(947\) | −567.925 | + | 327.891i | −0.599709 | + | 0.346242i | −0.768927 | − | 0.639336i | \(-0.779209\pi\) |
0.169218 | + | 0.985579i | \(0.445876\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.5694 | + | 39.0914i | −0.0237823 | + | 0.0411922i | ||||
\(950\) | 385.638 | + | 314.346i | 0.405935 | + | 0.330890i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −823.052 | + | 35.1641i | −0.864551 | + | 0.0369371i | ||||
\(953\) | −554.778 | −0.582139 | −0.291069 | − | 0.956702i | \(-0.594011\pi\) | ||||
−0.291069 | + | 0.956702i | \(0.594011\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 767.193i | − | 0.803344i | ||||||
\(956\) | −987.373 | + | 203.234i | −1.03282 | + | 0.212588i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1006.04 | − | 820.055i | −1.05015 | − | 0.856007i | ||||
\(959\) | 453.102 | + | 261.599i | 0.472474 | + | 0.272783i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −343.493 | − | 594.947i | −0.357432 | − | 0.619091i | ||||
\(962\) | 47.5490 | + | 7.68808i | 0.0494272 | + | 0.00799177i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1715.98 | + | 569.801i | 1.78006 | + | 0.591080i | ||||
\(965\) | −411.009 | − | 711.889i | −0.425917 | − | 0.737709i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −502.000 | − | 289.830i | −0.519131 | − | 0.299720i | 0.217448 | − | 0.976072i | \(-0.430227\pi\) |
−0.736579 | + | 0.676351i | \(0.763560\pi\) | |||||||
\(968\) | −159.128 | + | 101.167i | −0.164388 | + | 0.104511i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −13.8455 | − | 36.4189i | −0.0142737 | − | 0.0375452i | ||||
\(971\) | − | 260.660i | − | 0.268445i | −0.990951 | − | 0.134223i | \(-0.957146\pi\) | ||
0.990951 | − | 0.134223i | \(-0.0428537\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1750.76 | −1.79934 | ||||||||
\(974\) | −527.382 | + | 200.497i | −0.541460 | + | 0.205849i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1072.83 | − | 461.189i | 1.09921 | − | 0.472530i | ||||
\(977\) | −638.953 | + | 1106.70i | −0.653995 | + | 1.13275i | 0.328149 | + | 0.944626i | \(0.393575\pi\) |
−0.982145 | + | 0.188127i | \(0.939758\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 553.793 | − | 319.732i | 0.565672 | − | 0.326591i | ||||
\(980\) | −880.143 | − | 292.257i | −0.898105 | − | 0.298221i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 240.680 | − | 1488.55i | 0.245092 | − | 1.51584i | ||||
\(983\) | 378.325 | − | 218.426i | 0.384868 | − | 0.222204i | −0.295066 | − | 0.955477i | \(-0.595342\pi\) |
0.679934 | + | 0.733273i | \(0.262008\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 188.746 | − | 326.918i | 0.191621 | − | 0.331897i | ||||
\(986\) | −228.373 | + | 280.167i | −0.231615 | + | 0.284145i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −32.7211 | + | 6.73510i | −0.0331185 | + | 0.00681690i | ||||
\(989\) | −785.562 | −0.794300 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1344.50i | − | 1.35671i | −0.734734 | − | 0.678356i | \(-0.762693\pi\) | ||
0.734734 | − | 0.678356i | \(-0.237307\pi\) | |||||||
\(992\) | 509.385 | + | 145.320i | 0.513493 | + | 0.146492i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1638.30 | + | 2009.86i | −1.64819 | + | 2.02200i | ||||
\(995\) | −26.3858 | − | 15.2338i | −0.0265184 | − | 0.0153104i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 942.397 | + | 1632.28i | 0.945233 | + | 1.63719i | 0.755284 | + | 0.655398i | \(0.227499\pi\) |
0.189949 | + | 0.981794i | \(0.439168\pi\) | |||||||
\(998\) | 164.464 | − | 1017.17i | 0.164794 | − | 1.01921i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 108.3.f.c.91.3 | 16 | ||
3.2 | odd | 2 | 36.3.f.c.31.6 | yes | 16 | ||
4.3 | odd | 2 | inner | 108.3.f.c.91.2 | 16 | ||
8.3 | odd | 2 | 1728.3.o.g.1279.6 | 16 | |||
8.5 | even | 2 | 1728.3.o.g.1279.5 | 16 | |||
9.2 | odd | 6 | 36.3.f.c.7.7 | yes | 16 | ||
9.4 | even | 3 | 324.3.d.g.163.8 | 8 | |||
9.5 | odd | 6 | 324.3.d.i.163.1 | 8 | |||
9.7 | even | 3 | inner | 108.3.f.c.19.2 | 16 | ||
12.11 | even | 2 | 36.3.f.c.31.7 | yes | 16 | ||
24.5 | odd | 2 | 576.3.o.g.319.3 | 16 | |||
24.11 | even | 2 | 576.3.o.g.319.6 | 16 | |||
36.7 | odd | 6 | inner | 108.3.f.c.19.3 | 16 | ||
36.11 | even | 6 | 36.3.f.c.7.6 | ✓ | 16 | ||
36.23 | even | 6 | 324.3.d.i.163.2 | 8 | |||
36.31 | odd | 6 | 324.3.d.g.163.7 | 8 | |||
72.11 | even | 6 | 576.3.o.g.511.3 | 16 | |||
72.29 | odd | 6 | 576.3.o.g.511.6 | 16 | |||
72.43 | odd | 6 | 1728.3.o.g.127.5 | 16 | |||
72.61 | even | 6 | 1728.3.o.g.127.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.3.f.c.7.6 | ✓ | 16 | 36.11 | even | 6 | ||
36.3.f.c.7.7 | yes | 16 | 9.2 | odd | 6 | ||
36.3.f.c.31.6 | yes | 16 | 3.2 | odd | 2 | ||
36.3.f.c.31.7 | yes | 16 | 12.11 | even | 2 | ||
108.3.f.c.19.2 | 16 | 9.7 | even | 3 | inner | ||
108.3.f.c.19.3 | 16 | 36.7 | odd | 6 | inner | ||
108.3.f.c.91.2 | 16 | 4.3 | odd | 2 | inner | ||
108.3.f.c.91.3 | 16 | 1.1 | even | 1 | trivial | ||
324.3.d.g.163.7 | 8 | 36.31 | odd | 6 | |||
324.3.d.g.163.8 | 8 | 9.4 | even | 3 | |||
324.3.d.i.163.1 | 8 | 9.5 | odd | 6 | |||
324.3.d.i.163.2 | 8 | 36.23 | even | 6 | |||
576.3.o.g.319.3 | 16 | 24.5 | odd | 2 | |||
576.3.o.g.319.6 | 16 | 24.11 | even | 2 | |||
576.3.o.g.511.3 | 16 | 72.11 | even | 6 | |||
576.3.o.g.511.6 | 16 | 72.29 | odd | 6 | |||
1728.3.o.g.127.5 | 16 | 72.43 | odd | 6 | |||
1728.3.o.g.127.6 | 16 | 72.61 | even | 6 | |||
1728.3.o.g.1279.5 | 16 | 8.5 | even | 2 | |||
1728.3.o.g.1279.6 | 16 | 8.3 | odd | 2 |